This paper considers a fluid queueing system, fed by N independent sources that alternate between silence and activity periods. We assume that the distribution of the activity periods of source 1 is a regularly varying function of index i , whereas all other sources have activity period distributions with an exponential tail. In addition, we assume that the inflow rate of each of the sources, when active, exceeds the outflow rate of the buffer. Under these assumptions, we show that the tail of the buffer content distribution is regularly varying of index i +1. In the special case that i 2 (\Gamma2; \Gamma1), which implies long-range dependence of the input process, the buffer content does not even have a finite first moment. Based on the obtained results and on a conjecture for the case that the outflow rate of the buffer is not necessarily exceeded by the inflow rates of the sources, we suggest a simple, effective-bandwidth-like, connection admission rule. AMS Subject Classi...